Transportation network with fluctuating input/output designed by the bio-inspired Physarum algorithm.

Watanabe S, Takamatsu A - PLoS ONE (2014)

Bottom Line:
This paper studies the design of network topology and traffic distribution with oscillatory input and output traffic flows.We observe various rich topologies such as complete mesh, partial mesh, Y-shaped, and V-shaped networks depending on this adaptation parameter and evaluate them on the basis of three performance functions: loss, cost, and vulnerability.We use stability analysis to reveal how the system exhibits various topologies depending on the parameter.

ABSTRACTIn this paper, we propose designing transportation network topology and traffic distribution under fluctuating conditions using a bio-inspired algorithm. The algorithm is inspired by the adaptive behavior observed in an amoeba-like organism, plasmodial slime mold, more formally known as plasmodium of Physarum plycephalum. This organism forms a transportation network to distribute its protoplasm, the fluidic contents of its cell, throughout its large cell body. In this process, the diameter of the transportation tubes adapts to the flux of the protoplasm. The Physarum algorithm, which mimics this adaptive behavior, has been widely applied to complex problems, such as maze solving and designing the topology of railroad grids, under static conditions. However, in most situations, environmental conditions fluctuate; for example, in power grids, the consumption of electric power shows daily, weekly, and annual periodicity depending on the lifestyles or the business needs of the individual consumers. This paper studies the design of network topology and traffic distribution with oscillatory input and output traffic flows. The network topology proposed by the Physarum algorithm is controlled by a parameter of the adaptation process of the tubes. We observe various rich topologies such as complete mesh, partial mesh, Y-shaped, and V-shaped networks depending on this adaptation parameter and evaluate them on the basis of three performance functions: loss, cost, and vulnerability. Our results indicate that consideration of the oscillatory conditions and the phase-lags in the multiple outputs of the network is important: The building and/or maintenance cost of the network can be reduced by introducing the oscillating condition, and when the phase-lag among the outputs is large, the transportation loss can also be reduced. We use stability analysis to reveal how the system exhibits various topologies depending on the parameter.

pone-0089231-g006: Comparison of the performances for the networks designed under constant and oscillatory conditions.A Ratio in loss, . B Ratio in cost, . Circles, triangles, and squares respectively denote . The data are those for the homogeneous initial conditions of .

Mentions:
To investigate the benefit derived from the introduction of the oscillatory condition, we calculated the ratio of the performances between the constant and oscillatory input/output, as shown in Fig. 6. Note that the performance and were estimated with oscillatory input/output against the networks obtained under constant condition by the Physarum algorithm. The performances and were estimated with oscillatory input/output against the networks obtained under the oscillatory condition, which are the same as those of Fig. 5.

pone-0089231-g006: Comparison of the performances for the networks designed under constant and oscillatory conditions.A Ratio in loss, . B Ratio in cost, . Circles, triangles, and squares respectively denote . The data are those for the homogeneous initial conditions of .

Mentions:
To investigate the benefit derived from the introduction of the oscillatory condition, we calculated the ratio of the performances between the constant and oscillatory input/output, as shown in Fig. 6. Note that the performance and were estimated with oscillatory input/output against the networks obtained under constant condition by the Physarum algorithm. The performances and were estimated with oscillatory input/output against the networks obtained under the oscillatory condition, which are the same as those of Fig. 5.

Bottom Line:
This paper studies the design of network topology and traffic distribution with oscillatory input and output traffic flows.We observe various rich topologies such as complete mesh, partial mesh, Y-shaped, and V-shaped networks depending on this adaptation parameter and evaluate them on the basis of three performance functions: loss, cost, and vulnerability.We use stability analysis to reveal how the system exhibits various topologies depending on the parameter.

ABSTRACTIn this paper, we propose designing transportation network topology and traffic distribution under fluctuating conditions using a bio-inspired algorithm. The algorithm is inspired by the adaptive behavior observed in an amoeba-like organism, plasmodial slime mold, more formally known as plasmodium of Physarum plycephalum. This organism forms a transportation network to distribute its protoplasm, the fluidic contents of its cell, throughout its large cell body. In this process, the diameter of the transportation tubes adapts to the flux of the protoplasm. The Physarum algorithm, which mimics this adaptive behavior, has been widely applied to complex problems, such as maze solving and designing the topology of railroad grids, under static conditions. However, in most situations, environmental conditions fluctuate; for example, in power grids, the consumption of electric power shows daily, weekly, and annual periodicity depending on the lifestyles or the business needs of the individual consumers. This paper studies the design of network topology and traffic distribution with oscillatory input and output traffic flows. The network topology proposed by the Physarum algorithm is controlled by a parameter of the adaptation process of the tubes. We observe various rich topologies such as complete mesh, partial mesh, Y-shaped, and V-shaped networks depending on this adaptation parameter and evaluate them on the basis of three performance functions: loss, cost, and vulnerability. Our results indicate that consideration of the oscillatory conditions and the phase-lags in the multiple outputs of the network is important: The building and/or maintenance cost of the network can be reduced by introducing the oscillating condition, and when the phase-lag among the outputs is large, the transportation loss can also be reduced. We use stability analysis to reveal how the system exhibits various topologies depending on the parameter.